On angles between subspaces of a finite dimensional inner product space

By Per-Åke Wedin. 1983

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Citations in the corpus

A Theoretical Analysis of Catastrophic Forgetting through the NTK Overlap Matrix (2020, background): “More formally, the singular values of O τ S → τ T SGD are the cosines of the principal angles between the spaces spanned by the source data φ ( X τ S ) and the target data φ ( X τ T ) [Wedin, 1983].”
Exploring the space of a human action (2005, background): “It was shown by Wedin in [11] that the angle betweenW andW′ gives an estimate of the amount of new information afforded by the second matrix not associated with measurement noise.”
Automatic acquisition of high-fidelity facial performances using monocular videos (2014, methodology): “The difference between the two PCA subspaces is measured by principal angle [Wedin 1983], and is experimentally set to 0.4.”
Semiparametric estimation of fractional cointegrating subspaces (2006, background): “For any nonzero vector x ∈M(S), the sine of the angle between x and the subspace M(T) is a real number defined as sinθ(x,M(T)) = ‖(I−TT )x‖ ‖x‖ , see [24], page 274.”
Geometric aspects of the theory of Krylov subspace methods (2001, unknown): “The connection between angles and orthogonal projections is given in the following lemma, a proof of which can be found in Wedin (1983), for example.”
Subspaces, angles and pairs of orthogonal projections (2008, unknown): “For other proofs of the Ljance result see, e.g. Buckholtz [17], Corach et al. [20], Galántai [32], Groß [40], Pták [79], Robinson [81], and Wimmer [91].”